5a) Find the values of p for which the equation x^2 + px + 8 = p has one positive and one negative root [p > 8]

I have found the determinant to be p^2 + 4p - 32

Please advise how to continue - the answer is not obtained by taking determinant > 0

b) Find the positive value of k for which the equation 6x^2 - 2kx + k = 0 has 2 real roots, one being thrice the other

I have found the determinant to be k^2 - 6k

Please advise how to proceed

c) Given that A and B are the roots of the euqation x^2 = 3x + 5, find the value of 1/A^2 + 1/B^2 and show that A^4 = 57A + 70

I have found the answer to be 19/25, but I've no idea how to show the equation

Please help!

Thanks a lot